[music-dsp] Re: Declipping

Bob Cain arcane at arcanemethods.com
Tue Feb 22 23:08:41 EST 2005



Nigel Redmon wrote:
>> The zero insertion is a distorting process wherein the distortion 
>> products all happen to be above the original band limit so that 
>> post-filtering it removes them and only them.  No?
> 
> 
> OK, but what is the rationale behind distorting the signal in this way? 

Exploit serendipity.

Only zeros force all the alias components to be outside the 
original baseband.

> If you treat the samples as impulses, inserting zeros isn't a 
> "technique"--it's just doing the obvious. I can explain the upsampling 
> process in a few sentences, using the impulse model, and I think it 
> would be pretty hard for you to come up with math that shows that the 
> results are flawed. 

I don't think it is flawed from an operational standpoint, I 
just find it incorrect to think of sampled data as only 
having values at the sample points.  There is a difference 
between what is being represented and the representation 
system itself.

> If you could explain how and why we choose to 
> distort the signal--that you view as continuous--with zeros, I'd be 
> interested to read it. I'm not saying that you can't come up with one, 
> but if it's simpler and more intuitive than my explanation, I'll be 
> impressed ;-) (Really, not trying to put you on the spot--just want you 
> to think it through.)

Again, we exploit the serendipitous fact that introducing 
that particular distortion leaves us with an easy way of 
removing what we don't want to be left with what we do want.

Question.  If you take the DFT of a sampled impulse response 
do you consider the values between the frequency domain 
samples to be zero?  If not, the domains being duals, why 
would one be so considered and the other not be?


Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein



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